Microwave transmission line and devices using multiple coplanar conductors

ABSTRACT

Three coplanar conductive surfaces on the top surface of a dielectric substrate form a microwave transmission line having first and second transmission modes used in the construction and operation of various microwave devices, such as amplifiers and directional couplers.

United States Patent De Brecht et al.

[ Nov. 12, 1974 MICROWAVE TRANSMISSION LINE AND DEVICES USING MULTIPLECOPLANAR CONDUCTORS Inventors: Robert Eugene De Brecht,

Cranbury; Louis Sebastian Napoli, Hamilton Square, both of NJ,

Assignee: RCA Corporation, New York, NY.

Filed: Sept. 27, 1973 Appl. No.: 401,553

Related U.S. Application Data Division ofSer. No. 3 l5,087 Dec. 14,1972, Pat. No. 3,708,575v

U.S. CI. 330/56, 333/24.l, 333/84 M Int. Cl. H03f 3/60 Field of Search330/56; 333/24.l, 84 M BALANCED TRANSMISSIONLINE\\ OUTPUT TERMINALS [56] References Cited UNITED STATES PATENTS 3,560,893 2/1971 Weh 333/24.l

Primary ExaminerNathan Kaufman Attorney, Agent, or FirmEdward J. Norton;Joseph D. Lazar; Donald E. Mahoney [57] ABSTRACT Three coplanarconductive surfaces on the top surface of a dielectric substrate form amicrowave transmission line having first and second transmission modesused in the construction and operation of various microwave devices,such as amplifiers and directional couplers.

3 Claims, 8 Drawing Figures UNBALANCED TRANSMISSION LINE \LNPUT TERMINALPATENTELHUVIZIQH sum 1 o 5 PRIOR ART PAlEmmrmmlsn 3.8486198 7 sum 2 0f 5EVEN MODE IMPEDANCE (OHMS) e,+| z I 5 8 PATENTEL NOV 1 2 I974 sum 3. g

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Pmammwv 2 M' A 3.848.198 suinupfg BALANCED TRANSMISSIONUNx OUTPUTTERMINALS MICROWAVE TRANSMISSION LINE AND DEVICES USING MULTIPLECOPLANAR CONDUCTORS This is a division, of application Ser. No. 315,087,

filed Dec. 14, 1972. Now US. Pat. No. 3798575.

DESCRIPTION OF THE PRIOR ART Existing microwave transmission linessuitable for microwave integrated circuits employ a strip-like conductoron the top surface of a dielectric substrate and a ground planarconductor on the bottom surface of the dielectric substrate. Microwaveenergy is confined substantially within the dielectric substrate and istransmitted from an input port to an output port in the TEM (transverseelectromagnetic) mode. Some microwave integrated circuits employ twoadjacent and coplanar strip-like conductors on the top surface of thedielectric substrate. The microwave transmission characteristics ofthese circuits are dependent on how the electric fields of the microwaveenergy are distributed between conductive surfaces on both sides of thesubstrate.

For certain devices, it is inconvenient and impractical to use'atransmission line having a ground planar conductor on the bottom surfaceof a dielectric substrate and one or two coplanar strip-like conductorson the top surface of the dielectric substrate. A prior art transmissionline described in US. Pat. No. 3,560,893 issued to Cheng Paul Wen onFeb. 2, 1971, describes the use of three coplanar and parallelstrip-like conductors on the top surface of a dielectric substrate.Microwave energy is transmitted along the three conductor transmissionlines in a first transmission mode that confines the electric field ofthe applied microwave energy between the center conductor and the twoouter ground potential conductors. Certain microwave devices require notonly the first transmission mode but a new second transmission mode thatconfines the field between the two outer conductors for efficientoperation.

SUMMARY OF THE INVENTION According to the present invention atransmission line for electromagnetic-energy comprising first, secondand third coplanar strip-like conductors having predetermined widthsadjacent to one surface of a dielectric substrate confine the electricfields of the electromagnetic energy substantially within the dielectricsubstrate in first and second transmission modes. The first conductorhas a first edge separated from an adjacent edge of the second conductorat a first relative electric potential by a first predetermined gap. Thefirst conductor also has a second edge, opposite the first edge, that isseparated from an adjacent edge of the third conductor at a secondrelative electric potential by a second predetermined gap. The first,second and third conductor widths, the dielectric constant of thedielectric substrate, and the first and second predetermined gaps arearranged to confine the electric fields of the electromagnetic energysubstantially within the dielectric substrate between the first andsecond conductors and between the first and third conductors in a firsttransmission mode and between the second and third conductors in asecond transmission mode.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a perspective view of aprior art electromagnetic energy transmission line.

FIG. 2 is a perspective view of a transmission line in accordance withone embodiment of the present invention.

FIG. 3 is a plot of the even mode impedance of the transmission lineshown in FIG. 2 as a function of the ratio of the transmission linedimensions, a /b the dielectric constant of the dielectric substrate andthe ratio of the transmission line dimensions c,-b /2a,.

FIG. 4 is a plot of the ratio of odd mode impedance to even modeimpedance as a function of the ratio of the transmission line dimensionsa, b,, the dielectric constant of the dielectric substrate and the ratioof the transmission line dimensions c b /2a FIG. 5 is a perspective viewof a coplanar conductor directional coupler in accordance with anotherembodiment of the present invention.

FIG. 6 is a perspective view of an unbalanced-tobalanced transmissionline transformer in accordance with another embodiment of the presentinvention.

FIG. 7 is a schematic representation of the unbalanced-to-balancedtransmission line transformer illustrated in FIG. 6.

FIG. 8 is a top view of a microwave transistor pushpull amplifier inaccordance with a still further embodiment of the present invention.

DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION Referring to FIG.1, there is shown a perspective view of a prior art electromagneticenergy transmission line. The transmission line comprises three coplanarstriplike conductors ll, 15 and 17 on the top surface 22 of a dielectricsubstrate 13. The prior art transmission line, illustrated in FIG. 1, isdescribed in US. Pat. No. 3,560,893 issued to Cheng Paul Wen on Feb. 2,1971. A single, thin relatively narrow strip-like conductor 11 isseparated by predetermined gaps from two relatively wide strip-likeconductors l5 and 17 both at the same R.F. and DC. ground potential. Theminimum width of the first relatively wide strip-like ground conductor15 is more than twice as wide as narrow strip-like conductor 11 and isspaced near to and parallel with coplanar narrow strip-like conductor11. The minimum width of the second relatively wide strip-like groundconductor 17 is likewise more than twice as wide as narrow striplikeconductor 11 and is spaced near to and parallel with coplanar narrowstrip-like conductor 11 but on the opposite side of narrow strip-likeconductor 11 relative to ground conductor 15. The top surface 22 ofdielectric substrate 13 having the three coplanar striplike conductorsll, 15 and 17 thereon is open to free space. The bottom surface 16 ofdielectric substrate 13 is likewise open to free space.

The distribution of the electric field of electromagnetic energy coupledto the transmission line from a source, not shown, is represented bydashed electric field lines 19. Electric field lines 19 are distributedonly between narrow strip-like conductor 11 and wider strip-likeconductors 15 and 17 along their entire lengths. Electric field lines 19are contained mainly within the dielectric substrate 13 between narrowstriplike conductor 11 and ground conductors 15 and 17. However, someelectric field lines 19, not shown, are distributed between conductor 11and conductors 15 and 17 in the free space region. The intensity of theelectric field within dielectric substrate 13 is dependent on themagnitude of the dielectric constant of dielectric substrate 13. Adiscontinuity in displacement current density at the interface betweendielectric substrate 13 and free space is produced by that portion ofelectric field 19 tangential to the air-dielectric boundary ondielectric surface 22. The discontinuity in displacement current ondielectric surface 22 produces an axial component of magnetic field,represented by dashed lines 20, associated with electric field 19. Aportion of the axial component of the magnetic field 20 at the interfacebetween dielectric substrate 13 and free space on surface 22 is in thedirection of propagation. The magnetic field 20 extends along both sidesof narrow conductor 11 and passes under narrow conductor 11. Thedistance, d, between conductors 15 and 17 is preferably less thanone-half wavelength at the operating frequency in order to prevent thetransmission of electromagnetic energy in undesired modes.

In order to distribute the electric field between narrow strip-likeconductor 11 and wider strip-like conductors 15 and 17, a difference inpotential must exist between narrow strip-like conductor 11 and widerstrip-like conductors 15 and 17. Since both wider striplike conductors land 17 are at the same R.F. and DC. ground potential, the boundaryconditions for establishing an electric field between conductors and 17does not exist. The characteristic impedance of the prior art threecoplanar strip-like conductor transmis sion line is dependent on theestablishment of an electric field between only narrow strip-likeconductor 11 and wider strip-like conductors 15 and 17.

Referring to FIG. 2, there is shown a perspective view of atransmisssion line 40 comprising three coplanar strip-like conductors21, and 27 on the top surface of a dielectric substrate 23 in accordancewith one embodiment of the present invention. Center strip-likeconductor 21 is separated by predetermined gaps from first and secondouter strip-like conductors, 25 and 27 having predetermined widths.First outer strip-like conductor 25 is spaced near to and parallel withcoplanar center strip-like conductor 21. Second outer strip-likeconductor 27 is spaced near to and parallel with coplanar centerstrip-like conductor 21 but on the opposite side of center strip-likeconductor 21 relative to first outer conductor 25. The top surface 35 ofdielectric substrate 23 having the three coplanar strip-like conductors21, 25 and 27 thereon as illustrated in FIG. 2 is open to free space.Unlike the prior art transmission line illustrated in FIG. 1, theminimum width of first and second outer conductors 25 and 27 accordingto the present invention is not limited to be at least twice as wide ascenter conductor 27. Contrary to the prior art arrangements, accordingto the present invention a difference in RF. potential is providedbetween outer conductors 25 and 27 in accordance with severalarrangements to be described.

Electromagnetic energy from a source, not shown, is coupled totransmission line 40. The distribution of the electric field of theelectromagnetic energy coupled to transmission line is represented bydashed electric field lines 29. Electromagnetic energy can betransmitted along transmission line 40 in a first transmission mode thatdistributes electric field lines 29 between center strip-like conductor21 and outer strip-like conductors 25 and 27 along their entire lengthssince a difference in R.F. potential exists between center striplikeconductor 21 and outer strip-like conductors 25 and 27. Electromagneticenergy can also be transmitted along transmission line 40 in a secondtransmission mode that distributes electric field lines 29 between onlyouter strip-like conductors 25 and 27. Conditions can be established aswill be apparent to those skilled in this art that would allowsimultaneous transmission of electromagnetic energy in both the firstand second transmission modes. it should be understood that the termsfirst and second' transmission modes designate for convenience ofdescription and the appended claims both the arrangements and the modesof operation of transmission line 40 according to the present invention.

A portion of electric field 29 is tangential to the airdielectricboundary on dielectric surface 35 and produces a discontinuity indisplacement current density at the interface between dielectricsubstrate 23 and free space, The discontinuity in displacement currenton dielectric surface 35 produces an axial component of magnetic field,represented by dashed lines 31, associated with electric field 29. Aportion of the axial component of the magnetic field 31 at the interfacebe tween dielectric substrate 23 and free space on surface 35 is in thedirection of propagation when the distance, d, between outer conductors25 and 27 is small compared to the electrical distance of one wavelengthat the operating frequency. Under these conditions, the magnetic fieldlines 31 extend along both sides of center conductor 21 and eventuallypass under center conductor 21 forming a closed magnetic loop having aportion in the direction of electromagnetic transmission, The magnitudeof the magnetic field 31 present at the airdielectric interface on oneside of center conductor 21 is not equal to the magnitude of themagnetic field 31 on the other side ofcenter conductor 31. if themagnetic field lines 31 were represented by magnetic field vectors, thevectors would appear at the air-dielectric interface on the top surfaceof dielectric substrate 23 between center conductor 21 and outerconductors 25 and 27. The vectors would have a magnitude and directionthat would define a condition of circular polarization existing on thetop surface of dielectric substrate 23 between center conductor 21 andouter conductors 25 and 27. The sense of circular polarization(clockwise or counterclockwise) would be the same if viewed on oppositesides of center conductor 21. This polarization condition is significantin the construction of microwave ferrite devices as described by Lax andButton in Chapter 12 of Microwave Ferrites and Ferrimagnetics,McGraw-Hill publication.

If the distance, d, between outer conductors 25 and 27 is larger thanthe electrical distance of one wavelength at the operating frequency,the axial component of magnetic field lines 31 form a closed loop aroundcenter conductor 21. Under this condition, the closed loop of magneticfield lines 31 around center conductor 21 is then transverse to thedirection of electromagnetic transmission.

The term even mode impedance, Z is used to identify the impedance oftransmission line 40 when electromagnetic energy is transmitted in thefirst transmission mode, viz when electric field lines 29 aredistributed between center strip-like conductor 21 and outer strip-likeconductors 25 and 27. The impedance Z refers to an even mode impedancehaving a magnitude dependent on the intensity of the electric fielddistribution between center conductor 21 and outer conductor 27. Theimpedance Z refers to an even mode impedance having a magnitudedependent on the intensity of the electric field distribution betweencenter conductor 21 and outer conductor 25.

Referring to FIG. 3, there is shown a graph of even mode impedance, Z interms of the relative dielectric constant, 6,, of dielectric substrate23 versus the ratio of the substrate dimensions, a /b shown in FIG. 2.The dimension a is the distance from the center line of center conductor21 to the edge of center conductor 21. The dimension b is the distancefrom the center line of center conductor 21 to the nearest edgepf outerconductor 25. The dimension C is the distance from the center line ofcenter conductor 21 to the furthest edge of outer conductor 25. Assumingthat the dimensions of strip-like conductors 21, 25 and 27 comprisingtransmission line 40 and the relative dielectric constant e, are known,the graph in FIG. 3 is useful for determining even mode impedance Zunder the condition that transmission line 40 is symmetrical or Z Z andthe substrate thickness, t, greater than 4 X b,. In other words, thedimensions b, and c determining the width of outer conductor 25 and thegap between center conductor 21 and outer conductor 25 in FIG. 2, alsocorrespond to the dimensions of the width of outer conductor 27 and thegap between center conductor 21 and outer conductor 27. The magnitude ofthe even mode impedance is independent of the thickness, 2, ofdielectric substrate 23 in FIG. 2 when thickness, t, exceeds 4 X b Theterm odd mode impedance, Z is used to identify the impedance oftransmission line 40 when it is transmitting electromagnetic energy inthe second transmission mode, viz., when electric field lines 29 aredistributed between only outer conductors 25 and 27.

Referring to FIG. 4, there is shown a graph of the ratio of odd modeimpedance to even mode impedance, Z /2 versus the ratio of the substratedimensions, a lb shown in FIG. 2. The graph in FIG. 4 is useful fordetermining odd mode impedance, Z knowing Z and the dimensions ofstrip-like conductors 21, 25 and 27 comprising transmission line 40provided either transmission line 40 is symmetrical or Z Z As explainedabove, transmission line 40 is symmetrical when the dimensions b and cdetermining the width of outer conductor 25 and the gap between centerconductor 21 and outer conductor 25 in FIG. 2 also correspond to thedimensions of the width of outer conductor 27 and the gap between centerconductor 21 and outer conductor 27. The magnitude of the odd modeimpedance is independent of the thickness, t, of the dielectricsubstrate 23 in FIG. 2 when thickness, t, exceeds 4 X b FIGS. 3 and 4illustrate that the even mode and odd mode impedances of transmissionline 40 in FIG. 2 vary as a function of the a/b ratio when transmissionline 40 has a predetermined ratio of outer conductor width to centerconductor width (c b /2a A transmission line for electromagnetic energycomprising three coplanar strip-like conductors on the top surface of adielectric substrate permits construction of passive devices requiring adetermination of even and odd mode impedances for improved operation.The disclosed transmission line configuration permits easy connection ofactive devices between centerconductor 21 and outer conductors 25 and 27as well as a similar connection of other passive components.

Referring to FIG. 5, there is shown a perspective view of a directionalcoupler, according to this invention, comprising three coplanarstrip-like conductors 51, 55 and 57 on the top surface of a dielectricsubstrate 53. A directional coupler is a passive microwave device usedfor dividing microwave energy coupled to an input port between twooutput ports. The propagation of microwave energy transmitted to eachoutput port is dependent on the desired coupling coefficient. Part ofthe energy reflected at the two output ports is directed to a fourthport usually terminated in an energy absorbing load. The design of adirectional coupler in terms of even mode, Z' and odd mode, Z impedancesis known being described by Matthaei, Young and Jones in Chapter 13 ofMicrowave Filters Impedance- Matching Networks, and Coupling Structures.The desired characteristics of a directional coupler (couplingcoefficient, bandwidth, etc.) are directional coupler design goalsdescribed in Chapter 13 of the above cited text and are used tocalculate the magnitude of Z' and Z The magnitude Z used in FIGS. 3 and4 is equivalent to Z 12. The magnitude of Z used in FIGS. 3 and 4 isequivalent to 2Z Thus, FIGS. 3 and 4 can be used to determine the widthsof conductors 51, 55 and 57 and the separation between center conductor51 and outer conductors 55 and 57 that would allow operation of adirectional coupler having desired operating characteristics.

FIG. 5 also illustrates a method of coupling microwave energy to andfrom a transmission line comprising three coplanar strip-like conductors51, 55 and 57 on the top surface 65 of dielectric substrate 53. Coaxialouter conductor 58 of coaxial connector 66 is connected to outerstrip-like conductor 57. Coaxial center conductor of connector 66 isconnected to the closest end of center strip-like conductor 51. Coaxialouter conductor 59 of coaxial connector 67 is connected to outerstrip-like conductor 57. Coaxial center conductor 71 of connector 67 isconnected to the closest end of center strip-like conductor 51. A lengthL of outer strip-like conductor 57 separates coaxial outer conductor 58of connector 66 from coaxial outer conductor 59 of connector 67. Thelength L is equivalent to an electrical length of substantially )t/4,where A is the wavelength determined by the equation:

C being the velocity of light in a vacuum, f the midband operatingfrequency and e, the relative dielectric constant of dielectricsubstrate 53.

Coaxial outer conductor 61 of coaxial connector 69 is connected to outerstrip-like conductor 55. Coaxial center conductor 73 of connector 69 isconnected to center strip-like conductor 51 at the same end as coaxialcenter conductor 70 of coaxial connector 66. Coaxial outer conductor 60of connector 68 is connected to outer strip-like conductor 55. Coaxialcenter conductor 72 of connector 68 is connected to center strip-likeconductor 51 at the same end as coaxial center conductor 71 of connector67. A length L of outer strip-like conductor 55 separates coaxial outerconductor 61 of connector 69 from coaxial outer conductor 60 ofconnector 68. The length L is equivalent to an electrical length ofsubstantially M4, where )t is the wavelength determined by equation (1).

Outer strip-like conductor 57 may be at the same D.C. potential as outerstrip-like conductor 55 if either coaxial outer conductors 58 or 59 isat the same D.C. potential as either of coaxial outer conductors 60 or61. However, outer strip-like conductors 55 and 57 are not at the sameRF. potential when coaxial outer conductors 58, 59, 60 and 61 areconnected to outer strip-like conductors 55 and 57 as illustrated inFIG. 5. Thus, by arranging the connections as just described, thepreviously discussed boundary conditions for exciting the even and oddmode impedances in a transmission line comprising three coplanarstrip-like conductors are preserved.

The length L of center strip-like conductor 51 is equivalent to anelectrical length of M4, where )t is the wavelength determined byequation (1). Center striplike conductor 51 is coextensive and parallelwith outer strip-like conductor 55 over length L and with outerstrip-like conductor 57 over length L It is well known that a microwavesignal coupled to an input port connector of a directional coupler maybe divided into two output signals that are coupled from two output portconnectors that are directly opposite the input port connector. Forexample, if a microwave signal is coupled to input port connector 66,part of the microwave signal is transmitted directly to directlyopposite output port connector 67 and part of the microwave signal iscoupled to directly opposite output port connector 69. Substantiallynone of the input microwave signal is coupled to diagonally oppositeconnector 68.

Referring to FIG. 6, there is shown according to this invention aperspective view of an unbalanced-tobalanced transmission linetransformer commonly referred to as a balun. The balun provides animpedance transformation from the impedance magnitude of the signalsource, not shown, coupled to the unbalanced transmission line inputterminal section 74 to the impedance magnitude of a load, not shown,coupled to the balanced transmission line output terminal section 78.The balanced transmission line output terminal section 78 consists oftwo coplanar strip-like conductors 79 and 80 on the top surface 95 ofdielectric substrate 75. The balun is designed to transmit energy to aload terminating conductors 79 and 80. The design of balun section R25determines the characteristic impedance of balanced transmission line 78and section 125 also provides a condition that establishes a phasedifference of 180 electrical degrees between conductors 79 and 80.

Unbalanced transmission line input terminal section 74 consists of anarrangement of three coplanar and parallel strip-like conductors 81, 85and 87 in the top surface 95 of dielectric substrate 75 more fullydescribed in US. Pat. No. 3,560,893 issued to C. P. Wen on Feb. 2, 1971.Relatively narrow strip-like center conductor 81 is separated bypredetermined gaps from two relatively wide strip-like conductors 85 and87 both at the same RF. and D.C. ground potential. One method ofestablishing the same RF. and DC. ground potential at conductors 85 and87 is to connect the outer conductor of a coaxial connector, not shown,to conductors 85 and 87 and the center conductor of the connector toconductor 81. The width, W, of outer conductors 85 and 87 is at leasttwice as wide as the width of center conductor 81. A length of mildiameter wire 76 is connected from outer conductor 85 to outer conductor87. Wire 76 is used to maintain the same RF. and D.C. ground potentialbetween outer strip-like conductors and 87 at the end of unbalancedtransmission line input terminal section 74.

Balun section 125 consists of three coplanar and parallel strip-likeconductors 81, 88 and 89 on the top surface of dielectric substrate 75.Center strip-like conductor 81 is separated by predetermined gaps fromouter strip-like conductors 88 and 89. One end of outer strip-likeconductor 88 is connected to outer strip-like conductor 87 near theconnection point of wire 76. The other end of conductor 88 is connectedto one end of strip-like conductor 77. The electrical length ofconductor 88 from the connection point of wire 76 to the connectionpoint of conductor 77 is substantially M4, where A is the wavelengthdetermined by equation l )v The electrical length of conductor 77 isnegligible. One end of center strip-like conductor 81 is connected tothe other end of strip-like conductor 77. One end of outer strip-likeconductor 89 is connected to outer strip-like conductor 85 near theconnection point of wire 76.

One end of strip-like conductor 79 of section 78 is connected toconductor 77 anywhere along the length of conductor 77. One end ofstrip-like conductor 80 of section 78 is illustrated in FIG. 6 as beingan extension of outer strip-like conductor 89. Such an arrangement isexemplary only of other possible arrangements. The end of strip-likeconductor 80 may be connected to conductor 89 anywhere along the end ofconductor 89.

Referring to FIG. 7, there is shown a schematic equivalent of section ofthe balun illustrated in FIG. 6. The impedance Z is the load impedanceterminating the balanced transmission line output terminal section 78.The schematic representation of section 125 is useful in explaining thedetermination of odd mode impedance, Z and even mode impedance, Znecessary for the design of a balun operative over a broad frequencyband. Section 125 is schematically illustrated as having a first shortcircuited transmission line stub section 100, having a characteristicimpedance 22 connected in shunt with a transmission line section 102having a characteristic impedance 22 A second short circuitedtransmission line stub section 101 having a characteristic impedance Zis also connected in shunt with transmission line section 102. Theelectrical length of transmission line section 102 separating theconnection points of sections I00 and NI to section 102 is substantiallyIt 4, where A is the wavelength defined by equation (1 The electricallength of sections 100 and 101 from their connection to section 102 totheir short circuited ends is substantiaily M4, where A is thewavelength defined in equation l The characteristic impedance, Z ofbalanced transmission line section 78 at mid-band frequency, 1",, is

{2) where Z is the even mode impedance of section 102 and Z is themagnitude of the impedance of the signal source, not shown, coupled tounbalanced transmission line section 74. At mid-band frequency, f,,, theshunt connected short circuited stub sections and X01 each appear as anopen circuit or very high impedance connected in shunt with section 102and thus do not affect the determination of balanced transmission linecharacteristic impedance Z At operating frequencies other than themid-band frequency, f,,, the characteristic impedance 2, of balancedtransmission line section 78 is:

where Z is the even mode impedance of section 102, Z is the odd modeimpedance of section 102, is the electrical length of stub sections 100and 101 at the operating frequency and Z is the magnitude of the signalsource, not shown, coupled to unbalanced transmission line section 74.Thus, the desired characteristic impedance 2,, of balanced outputterminal section 78 and its variations over a desired frequency band canbe determined from equations (2) and (3). The even mode impedance. Z andthe odd mode impedance, Z used in equations (2) and (3) together withthe graphs of FIGS. 3 and 4 may be used to determine the width ofstrip-like conductors 81, 88 and 89 and the spacing between centerconductor 81 and outer conductors 88 and 89 of the balun illustrated inFIG. 6.

Referring to FIG. 8, there is shown a top view of a microwave transistorpush-pull amplifier according to the invention, having all conductivesurfaces and transistors on the top surface 95 of a dielectricsubstrate. The push-pull amplifier uses the balun illustrated in FIG. 6as push-pull amplifier input transformer 103 and pushpull amplifieroutput transformer 104. For convenience, the numbers identifying theconductive surfaces of the balun illustrated in FIG. 6 are used toidentify the conductive surfaces of input and output pushpull amplifiertransformers 103 and 104. A detailed explanation of push-pulltransformer-coupled power amplifiers is disclosed in Section 4.2 ofElectronic Designers Handbook by Landee, Davis and Albrecht.

Gate electrode 105 of transistor T, is connected to balancedtransmission line terminal 80 of input balun 103 and gate electrode 106of transistor T is connected to balanced transmission line terminal 79of input balun 103. Source electrode 107 of transistor T, and sourceelectrode 108 of transistor T are connected to strip-like conductors 109which are at DC. ground potential. As previously discussed, in thedescription of the balun illustrated in FIG. 6, the widths of strip-likeconductors 81, 88 and 89 and the separation between inner conductor 81and outer conductors 88 and 89 of input of input balun 103 aredetermined from FIGS. 3 and 4 when the magnitudes of even modeimpedance, Z and odd mode impedance, Z are known. Equations (2) and (3)are used to determine the magnitudes of Z and Z necessary for the properimpedance transformation from the known impedance of the input signalsource, not shown, to the known input impedance magnitude of transistorsT, and T As an example, the impedance of the input signal source is 50ohms and the magnitude of the combined input impedance of transistors T,and T, is substantially 200 ohms. The relative dielectric constant, 6,,of the dielectric substrate is 2.2. The width of center strip-likeconductor 81 of balun 103 is 0.020 inches. The widths of outerstrip-like conductors 88 and 89 of balun 103 is 0.020 inches. Theseparation between center strip-like con- 1 ductor 81 and outerstrip-like conductors 88 and 89 of balun 103 is 0.028 inches.

Drain electrode 110 of transistor T, is connected to balancedtransmission line terminal of output balun 104 and drain electrode 126of transistor T is connected to balanced transmission line terminal 79of output balun 104. The widths of strip-like conductors 81, 88 and 89and the separation between inner conductor 81 and outer conductors 88and 89 of output balun 104 are determined from FIGS. 3 and 4 when themagnitudes of even mode impedance, Z and odd mode impedance, Z areknown. Equations (2) and (3) are used to determine the magnitudes of Zand Z necessary for the proper impedance transformation from the outputimpedance magnitude of transistors T, and T to the impedance magnitudeof the load, not shown, terminating the output signal port. As anexample, the impedance of the terminating output load is 50 ohms and themagnitude of the combined output impedance of transistors T, and T issubstantially 450 ohms. The width of center strip-like conductor 81 ofbalun 104 is 0.016 inches. The widths of outer strip-like conductors 88and 89 of balun 104 is 0.016 inches. The separation between centerstrip-like conductor 81 and outer strip-like conductors 88 and 89 ofbalun 104 is 0.035 inches.

A negative DC. bias voltage of 2 volts is applied to gates 105 and 106of Gallium Arsenide Schottkybarrier FET (Field Effect Transistor)transistors T, and T A positive DC. bias voltage of 5 volts is appliedto drains 110 and 126 of transistors T, and T The gain of the push-pullamplifier was 1.5 db over a 1.0 GHZ band of frequencies centered at 5.2GHz. The magnitude of the output power was 20 mw and the efficiency ofthe amplifier was 13 percent.

What is claimed is:

1. Apparatus for amplifying electromagnetic energy over a predeterminedband of frequencies comprising:

a dielectric substrate having a predetermined dielectric constant;

an input circuit having first, second and third coplanar strip-likeconductors each having input and output ends and predetermined widthsand lengths adjacent to one surface of said dielectric substrate, saidfirst conductor having one edge separated from an adjacent edge of saidsecond conductor by a first predetermined gap and an edge opposite saidone edge separated from an adjacent edge of said third conductor by asecond predetermined gap;

means for establishing a predetermined D.C. potential at said input endsrespectively of said second and third conductors of said input circuit,whereby said first, second and third conductor input ends, saiddielectric constant and said first and second predetermined gaps form anunbalanced transmission line input terminal:

means for connecting said output ends of said second and firstconductors of said input circuit, whereby said first and secondconductor output connected ends, said third conductor output end, saiddielectric constant and said first and second predetermined gaps form abalanced transmission line input terminal;

an output circuit having first, second and third coplanar strip-likeconductors each having input and output ends and predetermined widthsand lengths adjacent to one surface of said substrate, said firstconductor of said output circuit being separated from an adjacent edgeof said second conductor by a first predetermined gap and an edgeopposite said one edge separated from an adjacent edge of said thirdconductor by a second predetermined gap;

means for establishing a predetermined D.C. potential at said outputends of said second and third conductors of said output circuit, wherebysaid first, second and third conductor output ends of said outputcircuit, said dielectric constant, and said first and secondpredetermined gaps of said output circuit form an unbalancedtransmission line input tenninal;

means for connecting said input ends of said second and first conductorsof said output circuit, whereby said first and second conductor inputconnected ends of said output circuit, said third conductor input end,said dielectric constant and said first and second predetermined gaps ofsaid output circuits form a balanced transmission line input terminal;

a first electromagnetic energy amplifying device having a firstelectrode coupled to said third conductor output end of said inputcircuit, a second electrode coupled to said third conductor input end ofsaid output circuit and a third electrode at said predetermined DC.potential;

:1 second electromagnetic energy amplifying device having a firstelectrode coupled to said first and second conductor output connectedends of said input circuit, a second electrode coupled to said first andsecond conductor input connected ends of said output circuit and a thirdelectrode at said do. potential.

2. Apparatus according to claim 1, wherein said input circuit first,second and third conductors each have an electrical length between saidinput and output ends of substantially M4, where It is the wavelength atthe center freqeuncy of said band of frequencies.

3. Apparatus according to claim 1, wherein said output circuit first,second and third conductors each have an electrical length between saidinput and output ends of substantially M4, where )t is the wavelength atthe center frequency of said band of frequencies.

1. Apparatus for amplifying electromagnetic energy over a predeterminedband of frequencies comprising: a dielectric substrate having apredetermined dielectric constant; an input circuit having first, secondand third coplanar striplike conductors each having input and outputends and predetermined widths and lengths adjacent to one surface ofsaid dielectric substrate, said first conductor having one edgeseparated from an adjacent edge of said second conductor by a firstpredetermined gap and an edge opposite said one edge separated from anadjacent edge of said third conductor by a second predetermined gap;means for establishing a predetermined D.C. potential at said input endsrespectively of said second and third conductors of said input circuit,whereby said first, second and third conductor input ends, saiddielectric constant and said first and second predetermined gaps form anunbalanced transmission line input terminal: means for connecting saidoutput ends of said second and first Conductors of said input circuit,whereby said first and second conductor output connected ends, saidthird conductor output end, said dielectric constant and said first andsecond predetermined gaps form a balanced transmission line inputterminal; an output circuit having first, second and third coplanarstriplike conductors each having input and output ends and predeterminedwidths and lengths adjacent to one surface of said substrate, said firstconductor of said output circuit being separated from an adjacent edgeof said second conductor by a first predetermined gap and an edgeopposite said one edge separated from an adjacent edge of said thirdconductor by a second predetermined gap; means for establishing apredetermined D.C. potential at said output ends of said second andthird conductors of said output circuit, whereby said first, second andthird conductor output ends of said output circuit, said dielectricconstant, and said first and second predetermined gaps of said outputcircuit form an unbalanced transmission line input terminal; means forconnecting said input ends of said second and first conductors of saidoutput circuit, whereby said first and second conductor input connectedends of said output circuit, said third conductor input end, saiddielectric constant and said first and second predetermined gaps of saidoutput circuits form a balanced transmission line input terminal; afirst electromagnetic energy amplifying device having a first electrodecoupled to said third conductor output end of said input circuit, asecond electrode coupled to said third conductor input end of saidoutput circuit and a third electrode at said predetermined D.C.potential; a second electromagnetic energy amplifying device having afirst electrode coupled to said first and second conductor outputconnected ends of said input circuit, a second electrode coupled to saidfirst and second conductor input connected ends of said output circuitand a third electrode at said d.c. potential.
 2. Apparatus according toclaim 1, wherein said input circuit first, second and third conductorseach have an electrical length between said input and output ends ofsubstantially lambda /4, where lambda is the wavelength at the centerfreqeuncy of said band of frequencies.
 3. Apparatus according to claim1, wherein said output circuit first, second and third conductors eachhave an electrical length between said input and output ends ofsubstantially lambda /4, where lambda is the wavelength at the centerfrequency of said band of frequencies.